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These lecture notes aim at a post-Bachelor audience with a background at anintroductory level in Applied Mathematics and Applied Statistics. They discussthe logic and methodology of the Bayes-Laplace approach to inductivestatistical inference that places common sense and the guiding lines of thescientific method at the heart of systematic analyses of quantitative-empiricaldata. Following an exposition of exactly solvable cases of single- andtwo-parameter estimation problems, the main focus is laid on Markov Chain MonteCarlo (MCMC) simulations on the basis of Hamiltonian Monte Carlo sampling ofposterior joint probability distributions for regression parameters occurringin generalised linear models for a univariate outcome variable. The modellingof fixed effects as well as of correlated varying effects via multi-levelmodels in non-centred parametrisation is considered. The simulation ofposterior predictive distributions is outlined. The assessment of a model'srelative out-of-sample posterior predictive accuracy with informationentropy-based criteria WAIC and LOOIC and model comparison with Bayes factorsare addressed. A brief discussion on the description of the generation ofstationary time series data by means of autoregressive models is contained.Concluding, a conceptual link to the behavioural subjective expected utilityrepresentation of a single decision-maker's choice behaviour in static one-shotdecision problems is established. Vectorised codes for MCMC simulations ofmulti-dimensional posterior joint probability distributions with the Stanprobabilistic programming language implemented in the statistical software Rare provided. The lecture notes are fully hyperlinked. They direct the readerto original scientific research papers, online resources on inductivestatistical inference, and to pertinent biographical information.

An Introduction to Inductive Statistical Inference: from Parameter Estimation to Decision-Making